Multichannel or multi-input multi-output multirate filtering is discussed. Vector multirate systems are defined, and the issues of aliasing cancellation and perfect reconstruction are addressed in the vector context. The conditions for a vector linear periodically time-variant system to become time-invariant are derived. The idea of doubly complementary filters is generalized to the vector context, and one method for constructing doubly complementary filters is outlined. The construction of a vector perfect reconstruction system is briefly described